This open access textbook presents a comprehensive treatment of the arithmetic theory of
quaternion algebras and orders, a subject with applications in diverse areas of mathematics …

We review the present status of gauge theories built on various quantum space–times
described by noncommutative space–times. The mathematical tools and notions underlying …

'Der Kopf, so gesehen, hat mit dem Kopf, so gesehen, auch nicht die leiseste Ahnlichkeit (...)
Der Aspektwechsel.“Du würdest doch sagen, dass sich das Bild jetzt gänzlich geändert hat!” …

We survey the mathematical foundations of geometric deep learning, focusing on group
equivariant and gauge equivariant neural networks. We develop gauge equivariant …

We develop an operational framework, combining relativistic quantum measurement theory
with quantum reference frames (QRFs), in which local measurements of a quantum field on …

We experimentally achieve wave-mode conversion and rainbow trap** in an elastic
waveguide loaded with an array of resonators. Rainbow trap** is a phenomenon that …

Vladimir I. Bogachev Oleg G. Smolyanov Page 1 Moscow Lectures 4 Real and Functional
Analysis Vladimir I. Bogachev Oleg G. Smolyanov Page 2 Moscow Lectures Volume 4 Series …

We develop a random batch Ewald (RBE) method for molecular dynamics simulations of
particle systems with long-range Coulomb interactions, which achieves an O(N) complexity …

Abstract Liouville Conformal Field Theory (LCFT) on the disk describes the conformal factor
of the quantum disk, which is the natural random surface in Liouville quantum gravity with …

We consider the propagation and mode conversion of flexural-acoustic waves along a fluid-
loaded graded array of elastic resonators, forming a metasurface. The multi-physics nature …